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# Extreme lower probabilities

Erik Quaeghebeur (UGent) and Gert De Cooman (UGent)
(2008) 159(16). p.2163-2175
Author
Organization
Abstract
We consider lower probabilities on finite possibility spaces as models for the uncertainty about the state. These generalizations of classical probabilities can have some interesting properties; for example: k-monotonicity, avoiding sure loss, coherence, permutation invariance. The sets formed by all the lower probabilities satisfying zero or more of these properties are convex. We show how the extreme points and rays of these sets ─ the extreme lower probabilities ─ can be calculated and we give an illustration of our results.
Keywords
Extreme points, Lower probabilities, Imprecise probabilities, Non-additive measures, Combinatorial problems

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## Citation

Chicago
Quaeghebeur, Erik, and Gert De Cooman. 2008. “Extreme Lower Probabilities.” Fuzzy Sets and Systems 159 (16): 2163–2175.
APA
Quaeghebeur, E., & De Cooman, G. (2008). Extreme lower probabilities. Fuzzy Sets and Systems, 159(16), 2163–2175.
Vancouver
1.
Quaeghebeur E, De Cooman G. Extreme lower probabilities. Fuzzy Sets and Systems. 2008;159(16):2163–75.
MLA
Quaeghebeur, Erik, and Gert De Cooman. “Extreme Lower Probabilities.” Fuzzy Sets and Systems 159.16 (2008): 2163–2175. Print.
```@article{429244,
abstract     = {We consider lower probabilities on finite possibility spaces as models for the uncertainty about the state. These generalizations of classical probabilities can have some interesting properties; for example: k-monotonicity, avoiding sure loss, coherence,  permutation invariance. The sets formed by all the lower probabilities satisfying zero or more of these properties are convex. We show how the extreme points and rays of these sets \unmatched{2500} the extreme lower probabilities \unmatched{2500} can be calculated and we give an illustration of our results.},
author       = {Quaeghebeur, Erik and De Cooman, Gert},
issn         = {0165-0114},
journal      = {Fuzzy Sets and Systems},
keyword      = {Extreme points,Lower probabilities,Imprecise probabilities,Non-additive measures,Combinatorial problems},
language     = {eng},
number       = {16},
pages        = {2163--2175},
title        = {Extreme lower probabilities},
url          = {http://dx.doi.org/10.1016/j.fss.2007.11.020},
volume       = {159},
year         = {2008},
}

```
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